Major and minor triads - Revision history

Overthink: /* In just intonation */ lower limits should be first

2025-11-30T05:07:48Z

In just intonation: lower limits should be first

← Older revision		Revision as of 05:07, 30 November 2025
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	A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth.		A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth.

	In the 7-limit:		In the 3-limit:

	* [[14:18:21]], ~~a ''supermajor triad''~~, ~~is a~~ [[~~9-odd-limit~~]] ~~chord that tunes the third sharper than the 5-limit major~~.		* [[64:81:96]] is found on the I, IV, and V of the Pythagorean [[5L 2s\|diatonic scale]].

	In the 5-limit:		In the 5-limit:
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	* [[4:5:6]] is found on the I ({{Frac\|1\|1}}), IV ({{Frac\|4\|3}}), and V ({{Frac\|3\|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]).		* [[4:5:6]] is found on the I ({{Frac\|1\|1}}), IV ({{Frac\|4\|3}}), and V ({{Frac\|3\|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]).

	In the 3-limit:		In the 7-limit:

	* [[64:81:96]] ~~is found on the I~~, IV, ~~and V of the Pythagorean~~ [[~~5L 2s\|diatonic scale~~]].		* [[14:18:21]], a ''supermajor triad'', is a [[9-odd-limit]] chord that tunes the third sharper than the 5-limit major.

	=== Simple minor triads ===		=== Simple minor triads ===
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	A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.		A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.

	In the [[7-limit]]:		In the [[3-limit]]:
	* [[6:7:9]], ~~a ''subminor triad''~~, ~~is a [[9-odd-limit]] chord that tunes the third flatter than~~ the ~~5-limit minor~~.		* [[54:64:81]] is found on the ii ({{Frac\|9\|8}}), iii ({{Frac\|81\|64}}), and vi ({{Frac\|27\|16}}) of the Pythagorean diatonic scale.

	In the [[5-limit]]:		In the [[5-limit]]:
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	* [[27:32:40]] is found on the ii ({{Frac\|9\|8}}) of Ptolemy's intense diatonic scale.		* [[27:32:40]] is found on the ii ({{Frac\|9\|8}}) of Ptolemy's intense diatonic scale.

	In the [[3-limit]]:		In the [[7-limit]]:
	* [[54:64:81]] is ~~found on~~ the ~~ii ({{Frac\|9\|8}}), iii ({{Frac\|81\|64}}), and vi ({{Frac\|27\|16}}) of~~ the ~~Pythagorean diatonic scale~~.		* [[6:7:9]], a ''subminor triad'', is a [[9-odd-limit]] chord that tunes the third flatter than the 5-limit minor.

	== SCL files ==		== SCL files ==

VectorGraphics at 02:49, 14 April 2025

2025-04-14T02:49:05Z

← Older revision		Revision as of 02:49, 14 April 2025
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	In terms of [[mediant (tonality)\|latitude]], these triads tend to range from ±5-25°, corresponding to simple [[5-limit\|classical]] or [[7-limit\|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.		In terms of [[mediant (tonality)\|latitude]], these triads tend to range from ±5-25°, corresponding to simple [[5-limit\|classical]] or [[7-limit\|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.

	As interval regions, [[Minor third (interval region)\|minor thirds]] and [[Major third (interval region)\|major thirds]] range from, at the widest, 240-340c and 360-460c, although people tend to restrict this further, such as to roughly 260-330c and 370-440c.		As interval regions, [[Minor third (interval region)\|minor thirds]] and [[Major third (interval region)\|major thirds]] range from, at the widest, 240-340c and 360-460c, although people tend to restrict this further, such as to roughly 260-330c and 370-440c. And as an interval region, [[Perfect fifth\|perfect fifths]] range from around 660 to 740 cents at the widest, often being restricted to 680-720 cents.

	== In just intonation ==		== In just intonation ==

VectorGraphics at 02:48, 14 April 2025

2025-04-14T02:48:12Z

← Older revision		Revision as of 02:48, 14 April 2025
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	== In tempered scales ==		== In tempered scales ==
	In [[5L 2s\|diatonic (5L 2s) scales]], "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.		In [[5L 2s\|diatonic (5L 2s) scales]], "[[Major third (diatonic interval category)\|major third]]" and "[[Minor third (diatonic interval category)\|minor third]]" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.

	* In [[12edo]], major is 400{{cent}} and minor is 300{{cent}}.		* In [[12edo]], major is 400{{cent}} and minor is 300{{cent}}.
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	In terms of [[mediant (tonality)\|latitude]], these triads tend to range from ±5-25°, corresponding to simple [[5-limit\|classical]] or [[7-limit\|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.		In terms of [[mediant (tonality)\|latitude]], these triads tend to range from ±5-25°, corresponding to simple [[5-limit\|classical]] or [[7-limit\|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.

			As interval regions, [[Minor third (interval region)\|minor thirds]] and [[Major third (interval region)\|major thirds]] range from, at the widest, 240-340c and 360-460c, although people tend to restrict this further, such as to roughly 260-330c and 370-440c.

	== In just intonation ==		== In just intonation ==

VectorGraphics at 02:46, 14 April 2025

2025-04-14T02:46:25Z

← Older revision		Revision as of 02:46, 14 April 2025
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	* In [[22edo]], major is 436{{c}} and minor is 273{{c}}.		* In [[22edo]], major is 436{{c}} and minor is 273{{c}}.
	* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300{{c}} and minor at 375{{c}}, leading to the controversial "harmonic notation" of 16edo.		* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300{{c}} and minor at 375{{c}}, leading to the controversial "harmonic notation" of 16edo.
			** A more conventional interpretation labels the 300{{c}} third as "minor" and 375{{c}} as major, which is more sensible in terms of interval size and sound, despite technically not following Pythagorean notation.

	In terms of [[mediant (tonality)\|~~mediant~~]]s, ~~minor~~ triads tend to range ~~between a mediant of 37% and 47%, and major triads tend to range between 53% and 63%~~, corresponding to simple [[5-limit]] or septimal intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.		In terms of [[mediant (tonality)\|latitude]], these triads tend to range from ±5-25°, corresponding to simple [[5-limit\|classical]] or [[7-limit\|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.

	== In just intonation ==		== In just intonation ==

ArrowHead294 at 00:06, 24 February 2025

2025-02-24T00:06:50Z

← Older revision		Revision as of 00:06, 24 February 2025
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	== In tempered scales ==		== In tempered scales ==
			In [[5L 2s\|diatonic (5L 2s) scales]], "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.

	In [[5L 2s\|diatonic (5L 2s) scales]], "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.		* In [[12edo]], major is 400{{cent}} and minor is 300{{cent}}.
			* In [[19edo]], major is 379{{c}} and minor is 316{{c}}.
	* In [[12edo]], major is ~~400c~~ and minor is ~~300c~~.		* In [[22edo]], major is 436{{c}} and minor is 273{{c}}.
	* In [[19edo]], major is ~~379c~~ and minor is ~~316c~~.		* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300{{c}} and minor at 375{{c}}, leading to the controversial "harmonic notation" of 16edo.
	* In [[22edo]], major is ~~436c~~ and minor is ~~273c~~.
	* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at ~~300c~~ and minor at ~~375c~~, leading to the controversial "harmonic notation" of 16edo.

	In terms of [[mediant (tonality)\|mediant]]s, minor triads tend to range between a mediant of 37% and 47%, and major triads tend to range between 53% and 63%, corresponding to simple [[5-limit]] or septimal intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.		In terms of [[mediant (tonality)\|mediant]]s, minor triads tend to range between a mediant of 37% and 47%, and major triads tend to range between 53% and 63%, corresponding to simple [[5-limit]] or septimal intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.
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	== SCL files ==		== SCL files ==
	.SCL files for the classical major and minor triads are provided below<pre>! majortriad.scl		.SCL files for the classical major and minor triads are provided below:

			<pre>
			! majortriad.scl
	!		!
	The major triad as a wakalix		The major triad as a wakalix
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	3/2		3/2
	2/1		2/1
	</pre><pre>		</pre>
			<pre>
	! minortriad.scl		! minortriad.scl
	!		!
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	3/2		3/2
	2/1</pre>		2/1</pre>

	[[Category:Wakalixes]]		[[Category:Wakalixes]]
	[[Category:Triad]]		[[Category:Triad]]
	[[Category:Chords]]		[[Category:Chords]]
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]

Lériendil: transferred wikipedia references from old pages

2025-02-23T14:08:33Z

transferred wikipedia references from old pages

← Older revision		Revision as of 14:08, 23 February 2025
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	=== Simple major triads ===		=== Simple major triads ===
			{{Wikipedia\|Major chord}}

	A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth.		A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth.

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	=== Simple minor triads ===		=== Simple minor triads ===
			{{Wikipedia\|Minor chord}}

	A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.		A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.

Lériendil: moved definition around

2025-02-23T14:06:58Z

moved definition around

← Older revision		Revision as of 14:06, 23 February 2025
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	* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300c and minor at 375c, leading to the controversial "harmonic notation" of 16edo.		* If we pretend that [[16edo]]'s fifth generates a diatonic scale, this places major at 300c and minor at 375c, leading to the controversial "harmonic notation" of 16edo.

	In terms of ~~mediants, minor triads tend to range between a~~ [[mediant (tonality)\|mediant]] of 37% and 47%, and major triads tend to range between 53% and 63%, corresponding to simple [[5-limit]] or septimal intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.		In terms of [[mediant (tonality)\|mediant]]s, minor triads tend to range between a mediant of 37% and 47%, and major triads tend to range between 53% and 63%, corresponding to simple [[5-limit]] or septimal intervals. More extreme than major and minor are [[Extraclassical tonality\|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit\|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.

	== In just intonation ==		== In just intonation ==

Lériendil: clarified 5L 2s due to other uses of "diatonic" coöcurring below

2025-02-23T14:06:28Z

clarified 5L 2s due to other uses of "diatonic" coöcurring below

← Older revision		Revision as of 14:06, 23 February 2025
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	== In tempered scales ==		== In tempered scales ==

	In [[5L 2s\|diatonic scales]], "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.		In [[5L 2s\|diatonic (5L 2s) scales]], "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.

	* In [[12edo]], major is 400c and minor is 300c.		* In [[12edo]], major is 400c and minor is 300c.

Lériendil at 14:05, 23 February 2025

2025-02-23T14:05:58Z

← Older revision		Revision as of 14:05, 23 February 2025
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	=== Simple major triads ===		=== Simple major triads ===
			A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth.

	In the 7-limit:		In the 7-limit:

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	* [[64:81:96]] is found on the I, IV, and V of the Pythagorean [[5L 2s\|diatonic scale]].		* [[64:81:96]] is found on the I, IV, and V of the Pythagorean [[5L 2s\|diatonic scale]].

	== Simple minor triads ==		=== Simple minor triads ===
	A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.		A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth.

Lériendil: merged stuff on here

2025-02-23T14:04:58Z

merged stuff on here

@@ Line 1: / Line 1: @@
 Major and minor triads refer to [[triad]]s containing a [[perfect fifth|fifth]] alongside a [[major third|major]] and [[minor third]] respectively.
-== Approaches ==
+== In tempered scales ==
-In diatonic scales, "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.
+In [[5L 2s|diatonic scales]], "major third" and "minor third" are precisely defined intervals corresponding to [[81/64]] and [[32/27]] in [[Pythagorean tuning]], but generated by a tempered fifth.
 * In [[12edo]], major is 400c and minor is 300c.
@@ Line 12: / Line 11: @@
 In terms of mediants, minor triads tend to range between a [[mediant (tonality)|mediant]] of 37% and 47%, and major triads tend to range between 53% and 63%, corresponding to simple [[5-limit]] or septimal intervals. More extreme than major and minor are [[Extraclassical tonality|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads.
 == SCL files ==